TY - GEN

T1 - Spanners of additively weighted point sets

AU - Bose, Prosenjit

AU - Carmi, Paz

AU - Couture, Mathieu

N1 - Funding Information:
Research partially supported by NSERC , MRI , NETA , CFI , and MITACS .

PY - 2008/10/27

Y1 - 2008/10/27

N2 - We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p,r) where p is a point in the plane and r is a real number. The distance between two points (p i ,r i ) and (p j ,r j ) is defined as |p i p j |∈-∈r i ∈-∈r j . We show that in the case where all r i are positive numbers and |p i p j | ≥ r i ∈+∈r j for all i,j (in which case the points can be seen as non-intersecting disks in the plane), a variant of the Yao graph is a (1∈+∈ε)-spanner that has a linear number of edges. We also show that the Additively Weighted Delaunay graph (the face-dual of the Additively Weighted Voronoi diagram) has constant spanning ratio. The straight line embedding of the Additively Weighted Delaunay graph may not be a plane graph. Given the Additively Weighted Delaunay graph, we show how to compute a plane embedding with a constant spanning ratio in O(nlogn) time.

AB - We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p,r) where p is a point in the plane and r is a real number. The distance between two points (p i ,r i ) and (p j ,r j ) is defined as |p i p j |∈-∈r i ∈-∈r j . We show that in the case where all r i are positive numbers and |p i p j | ≥ r i ∈+∈r j for all i,j (in which case the points can be seen as non-intersecting disks in the plane), a variant of the Yao graph is a (1∈+∈ε)-spanner that has a linear number of edges. We also show that the Additively Weighted Delaunay graph (the face-dual of the Additively Weighted Voronoi diagram) has constant spanning ratio. The straight line embedding of the Additively Weighted Delaunay graph may not be a plane graph. Given the Additively Weighted Delaunay graph, we show how to compute a plane embedding with a constant spanning ratio in O(nlogn) time.

UR - http://www.scopus.com/inward/record.url?scp=54249084615&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-69903-3_33

DO - 10.1007/978-3-540-69903-3_33

M3 - Conference contribution

AN - SCOPUS:54249084615

SN - 3540699007

SN - 9783540699002

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 367

EP - 377

BT - Algorithm Theory - SWAT 2008 - 11th Scandinavian Workshop on Algorithm Theory, Proceedings

T2 - 11th Scandinavian Workshop on Algorithm Theory, SWAT 2008

Y2 - 2 July 2008 through 4 July 2008

ER -